Euclid: Optimising tomographic redshift binning for 3x2pt power spectrum constraints on dark energy

The tomographic approach to analysing the 3times2pt signal involves dividing the observed galaxy sample into a configuration of redshift bins. We present a simulation-based method to explore the optimum tomographic binning strategy for , focussing on the expected configuration of its first major data release (DR1). To do so, we 1) simulated a -like observation and generated mock shear catalogues from multiple realisations of the 3times2pt fields on the sky; and 2) measured the 3times2pt Pseudo-C_ ,w_ Euclid Euclid power spectra for a given tomographic configuration and derived the constraints they place on the standard dark energy equation-of-state parameters, (w_ a ). For a simulation including Gaussian-distributed photometric redshift uncertainties and shape noise under a ΛCDM cosmology, we find that bins that are equipopulated with galaxies yield the best constraints on (w_ ,w_ a ) for an analysis of the full 3times2pt signal or the angular clustering component only. For the cosmic shear component, the optimum (w_ ,w_ a ,w_ a ) contour and we conclude that the cosmic shear is relatively insensitive to the binning methodology. We find that the information gain extracted on(w_ ,w_ a )$ for any 3times2pt component starts to become saturated beyond roughly seven or eight bins. Any marginal gains resulting from a greater number of bins are likely to be limited by additional uncertainties present in a real measurement and the increasing demand for accuracy of the covariance matrix. Finally, we considered a 5% contamination from catastrophic photometric redshift outliers and found that if these errors are not mitigated in the analysis, the bias induced in the 3times2pt signal for ten equipopulated bins results in dark energy constraints that are inconsistent with the fiducial ΛCDM cosmology at gtrsim3,σ .